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George Boole: Mathematical Innovator and Reformer
| Article
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13751 |
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Section : |
NATURAL SCIENCE
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| Issue
Date : |
8 / 1988 |
3,017 Words |
| Author
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Ronald Calinger
Ronald Calinger is associate professor of history at The
Catholic University of America. He is the author of
Gottfried
Wilhelm Leibniz (1979) and editor of Classics of Mathematics
(1982). He has written more than 45 articles and reviews on
the history of mathematics and modern science. |
The computer revolution is transforming our technological society into an informational-technological one. Computers have proven to be valuable tools in such fields as commerce, education, science, journalism, and government. To cite but a few applications, computers are used to handle routine paperwork, automate industrial production, monitor medical conditions, and perform massive and complex computations.
Modern computers are divided into two classes: digital and analog. Digital computers are far more widely used because they are more powerful as a group and do not require higher mathematics for their operation.
By definition, digital computers rapidly manipulate symbols, not just numerals, to perform logical and arithmetical operations. They handle separate rather than continuous data, and operate much like technically improved finger-counting. Indeed, the name "digital" comes from the word digit. This, in turn, stems from the Latin word for finger, digitus.
Two steps taken in 1938 and 1946 were fundamental to the design of electronic digital computers. In 1938, American electrical engineer Claude Shannon successfully applied a calculus of reasoning based on Boolean algebra (algebra of logic)--with its determination of what lines of reasoning are valid, a two-valued system of operations, and binary variables 0 and 1--to design relay and switching circuits of digital computers. He recognized that, primarily, computer circuits perform logical functions, and that their electrical behavior is auxiliary. Not only were his ideas almost universally accepted in computer design, but because actions of relays and switches are analogous to modern electronic circuits on silicon chips, they also applied to the design of high-speed digital computers.
In 1946, Hungarian-born mathematician John von Neumann recommended that the binary number system be adopted for computers and that computers have internal storage for data. The binary system, with numerals 0 and 1, is based on powers of 2, while our decimal system is based on powers of 10. These systems have a one-to-one correspondence, as the following generation of binary numbers row by row in linear form indicates.
Most modern computers use the binary system for computations.
Therefore, in their design work Shannon and, to an extent, von Neumann drew upon the algebra of logic founded by
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